Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode Decomposition technique and the Iterative Filtering method. When a signal contains mono-components that have rapid varying instantaneous frequencies, we can think, for instance, to chirps or whistles, it becomes particularly hard for most techniques to properly factor out these components. The Adaptive Local Iterative Filtering technique has recently gained interest in many applied fields of research for being able to deal with non-stationary signals presenting amplitude and frequency modulation. In this work, we address the open question of how to guarantee a priori convergence of this technique, and propose two new algorithms. The first method, called Stable Adaptive Local Iterative Filtering, is a stabilized version of the Adaptive Local Iterative Filtering that we prove to be always convergent. The stability, however, comes at the cost of higher complexity in the calculations. The second technique, called Resampled Iterative Filtering, is a new generalization of the Iterative Filtering method. We prove that Resampled Iterative Filtering is guaranteed to converge a priori for any kind of signal. Furthermore, in the discrete setting, by leveraging on the mathematical properties of the matrices involved, we show that its calculations can be accelerated drastically. Finally, we present some artificial and real-life examples to show the powerfulness and performance of the proposed methods.

翻译：非静止信号在现实生活中是无处不在的。在过去几十年中,提出了许多技术,将多构件信号分解成简单的螺旋性单构件,例如破碎的模拟模式分解法和循环过滤法。当信号含有瞬间频率变化迅速的单构件时,我们可以想象,例如,对于大多数技术来说,它变得特别困难,很难正确地考虑到这些组成部分。适应性本地透析技术最近在许多应用的研究领域获得了兴趣,以便能够处理非静止信号,显示振动和频率调制。在这项工作中,我们讨论了如何保证这一技术事先趋同的开放问题,并提出了两种新的算法。第一个方法叫做“稳定性调整性本地透析过滤法”,它被证明总是可以相互趋同的。稳定性最近在许多应用的研究领域引起了新的复杂程度成本。第二个技术,叫做“恢复性循环”的精细化法,它被称作“预加固”的精细化法,它被显示的精细的精细的精细的精细化法。它被复制为“我们”的精细的精细的精细化法。它的精细的精细化法是,它的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细方法,它的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细法。